Some games award XP for very specific actions and achievements. In earlier editions of D&D you got XP equal to the gold value of treasure that you recovered. That's very clear and specific.
Later versions of D&D award XP for "overcoming challenges", which sounds pretty good, but in practice it pewters out because it's too vague. This has two effects. One is that killing monsters becomes by far the largest and most common source of XP awards because monsters have an unambiguous XP value right there in the book, black on white*. The other is that leveling up becomes vague. You know how much XP you got from monsters but not how much XP you got from other stuff. One of the most common houserules that I've seen in 3.x games over and over again is that you level up arbitrarily, whenever the GM (or group) feels it's appropriate.
This is good because it puts a very strong pacing tool into the hands of the players. It's also bad because it makes what is possibly the most important reward cycle in the D&D game arbitrary. We reward ourselves for...playing the game? The alternative is that you get rewarded for following the GM's story, leveling up at dramatically appropriate moments. That's ok for some kinds of games, but it doesn't fly with how I'm running Kalesh, which is why I've started thinking about XP in more detail.
Currently I see three alternatives:
1. Go back to the classic D&D formula of gold = xp. I'm not using Pathfinder treasure out of the books, not their implied economy, so this can't de-facto break the game. It would also focus gameplay considerably.
2.1. XP awarded for achievement of player-set goals. I really like this idea. It's very video-gamey in a way, cross-polinated with Keys or Beliefs from TSOY or Burning Wheel. Since this is a sandbox game (of the model described by the OSR, Eero's challenge-oriented play or Vincent's recent description of his LotFP games), the players set their own goals. Players decide on their own Quests (let's say you can have three "active" ones at any time, for the game's sake) and they either (a) gain a flat amount of XP every time they pursue the goal (not ideal, for various reasons) or (b) gain a pre-set amount of XP declared by the GM at the time they pick their Quest.*
2.2. Abandon XP altogether, much like in the "arbitrary level-up" house variant described above, except it's not arbitrary. In short, the conditions for the level up are negotiated up front. Players usually know what they want for the next level, so you can tell them what they'd have to do to get that. "If condition X is met, then you gain a level of Y."
*I commend 4E for giving traps an explicit XP value, but I think it doesn't go far enough. In terms of the gold:xp ratio I've also proposed the following some time in the past: magic items should have their own XP value. If the monsters are equipped with such (making the encounter more challenging), it is factored into their budget value. And when rewarding players you can dole out treasure instead of XP. (like, instead of 2000XP, the players get 1000XP and two magic items worth 500XP). This brings us to the following...
**This method would have to be balanced against treasure in some way. For example, let's say that the players decide their quest is capturing an incredibly valuable object - should that quest be worth more XP (because of the challenge) or less XP (because the treasure is its own reward).